Piketty's argument has been widely recounted. He has carefully investigated high-wealth tax returns in Europe and the United States and, deploying some intuitive reasoning, claims to have detected a central contradiction in capitalism.

Income inequality, rather than converging over time to make us more equal, actually diverges to make us less equal, and society therefore less meritocratic.

More formally, Piketty argues that the rate of return on capital (r) exceeds the rate of economic growth (g). That is, r > g.

As a consequence, rich investors accumulate wealth at a faster rate than ordinary income earners. That wealth is then passed on to their children. Over the long term, this creates an established permanent class of the super-rich, whose privilege cannot be justified by any meritocratic or utilitarian considerations.

It's a powerful story. The specifics of his model are debatable - see Paul Krugman's supportive review and Tyler Cowen's critical one - what's more interesting is what the book suggests is why we should worry about inequality.

The last line of Piketty's Capital is "Refusing to deal with numbers rarely serves the interests of the least well-off." This widely quoted aphorism is supposed to reflect his interest in empiricism. Yet it's quite misleading. The least well-off don't make much of an appearance in the book at all.

Capital offers a theory of the rich, not the poor. Specifically the very rich - the top 1 per cent of the population. They're the ones in his model about inherited wealth. However, the 9 per cent of people below that 1 per cent (that is, the rest of the richest 10 per cent) earned their wealth from income like the rest of us, not from capital investments and inheritance.

There are lots of potential reasons to care about inequality. The most obvious one is if high incomes lowered the incomes of those at the bottom of the scale. But outside some Marxist intellectual holdouts, there is no suggestion that the mere existence of the super-rich creates poverty.

No doubt some extreme incomes have come at the expense of the rest of society. In Russia the oligarchs have expropriated public wealth to become private wealth. In our liberal society, rent seeking or legal constructs like intellectual property can generate wealth at the expense of the rest of us.

But the issue in these cases is not the existence of the wealth but how it was taken. And the solution would be to close down the illegitimate means of acquiring that wealth.

So what of the poor? Piketty compares 19th century capitalism to 21st century capitalism and finds that they share roughly the same pattern of capital accumulation and inherited wealth. But even a casual observer of the historical record would understand that the big shifts in the interim century haven't been focused on the rich but on the poor.

Piketty is viscerally opposed to inequality. He says his story is "potentially terrifying". OK. But he doesn't get much more specific than that.

There are lots ways to measure inequality. If we look at inequality of consumption we see convergence rather than divergence. Where, in the past, only the rich could afford home heating, food refrigeration, personal transport, and to outsource chores like clothes washing, now those luxuries are shared by rich and poor alike. The living standards of the 19th century and those of today are virtually incomparable. (I made this argument on The Drum last Christmas.)

Good news for the poor, and all thanks to economic growth. Let's return to Piketty's formula: r > g. As he says this is not true at all times, but it is now, just as it was in the 19th century. Sometimes growth catches up to the rate of return on capital. Piketty believes we're in for a prolonged period of low growth. So does the Commonwealth Treasury. But doesn't that define the challenge?

The logic of his book suggests we ought to be single-mindedly trying to increase economic growth. Piketty dismisses a growth focus with a simple hand-wave. Yet it is surely no more an unrealistic goal than his alternative: a globally-imposed tax on capital to suppress extreme wealth.

And (here's a bonus!) a focus on growth above all else would directly help the poor.

Piketty is viscerally opposed to inequality. He says his story is "potentially terrifying". OK. But he doesn't get much more specific than that. A number of times in his book he fears wealth inequality will lead to political turmoil, even revolution. This dynamic isn't elaborated.

(A subsidiary concern he has is that high net wealth individuals dominate western culture. Maybe. But surely this applies better to the top 10 per cent rather than the inherited 1 per cent he focuses on.)

The philosopher John Rawls more concretely outlined what he saw was the ability of financial power to become social and political power. Yet if it is political power we are concerned with, then why not tackle political power directly? In New South Wales the ICAC has shown that wealth is neither a necessary nor sufficient condition to wield corrupt influence. It wasn't inherited riches that gave us Eddie Obeid.

The purpose of Piketty's proposed global capital tax isn't really to collect money for spending elsewhere. As he says there are so few high income individuals that even a very large tax would collect a small amount of money. Instead, its goal is simply to reduce the size of those honey pots.

There are lots of progressive reasons one might want to tax a population - for instance, social services or transfer payments. But simply because the government doesn't like people having lots of money seems like a very bad one.

Yet in context it makes sense. Piketty's book - and so much of the inequality debate more generally - seems to suggest that the core problem with inequality isn't that lots of people are poor, but that a few people are rich.

Chris Berg is a research fellow with the Institute of Public Affairs. Follow him at twitter.com/chrisberg. View his full profile here.